Partitioning Hadamard vectors into Hadamard matrices

preprint2016arXivOpen access

Abstract

We will show that in a space of dimension mm, any family of 2m−12^{m-1} distinct Hadamard vectors (where you can choose x or -x but not both) can be partitioned into Hadamard matrices if and only if m=2nm=2^n for some n. We will solve this problem with a simple algorithm for assigning the vectors to the Hadamard matrices.

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